Geodesic
Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes
Kybernetika, Tome 42 (2006) no. 5, pp. 539-556

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Doubly stochastic point processes driven by non-Gaussian Ornstein–Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.
Classification : 60G55, 60K35
Keywords: Cox process; filtering; Ornstein–Uhlenbeck process 
@article{KYB_2006__42_5_a1,
     author = {Proke\v{s}ov\'a, Michaela and Bene\v{s}, Viktor},
     title = {Nonlinear filtering in spatio{\textendash}temporal doubly stochastic point processes driven by {OU} processes},
     journal = {Kybernetika},
     pages = {539--556},
     publisher = {mathdoc},
     volume = {42},
     number = {5},
     year = {2006},
     mrnumber = {2283504},
     zbl = {1249.60097},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_5_a1/}
}
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Prokešová, Michaela; Beneš, Viktor. Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes. Kybernetika, Tome 42 (2006) no. 5, pp. 539-556. http://geodesic.mathdoc.fr/item/KYB_2006__42_5_a1/